Newsgroups: sci.nonlinear,comp.ai.philosophy,sci.cognitive
Path: cantaloupe.srv.cs.cmu.edu!das-news2.harvard.edu!news2.near.net!news.mathworks.com!uhog.mit.edu!bloom-beacon.mit.edu!news.media.mit.edu!minsky
From: minsky@media.mit.edu (Marvin Minsky)
Subject: Re: Obstructions to Shadowing
Message-ID: <1995Mar31.014130.8163@news.media.mit.edu>
Sender: news@news.media.mit.edu (USENET News System)
Organization: MIT Media Laboratory
References: <3levh8$r7i@portal.gmu.edu>
Date: Fri, 31 Mar 1995 01:41:30 GMT
Lines: 39
Xref: glinda.oz.cs.cmu.edu sci.nonlinear:2782 comp.ai.philosophy:26454 sci.cognitive:7129

In article <3levh8$r7i@portal.gmu.edu> herwin@osf1.gmu.edu (HARRY R. ERWIN) writes:
>Reference: Dawson, Grbogi, Sauer, and York, Obstructions to shadowing 
>when a Lyapunov exponent fluctuates about zero, Physical Review Letters, 
>75:14, 1927-1930.
>
>This paper investigates whether it is possible to find true trajectories
>of a chaotic dynamical system close to computer-generated trajectories. 
>The authors seem to claim that if the finite-time Lyapunov exponents of
>the system fluctuate about zero, then the system is ->intrinsically
>unshadowable<--i.e., any computational or symbolic model of the system
>will be invalid. Since it is just this type of fluctuation that occurs in
>the dynamics of neural activity in the brain during pattern
>classification, we get to an immediate conclusion that the brain cannot be
>validly modeled, i.e., John Searle and Roger Penrose are right. I'm not
>sure I believe this. 
>
>Comments?
>
>--
>Harry Erwin
>Internet: herwin@gmu.edu 

What could it possibly mean?  Does it mean that any two different runs
of the analog brain model would be more different from one another
than from all the runs of a computer simulation?  

Note that this question makes no sense without specifying a metric
over trajectories.  If you choose a low level metric on waveforms of
indivual cells, then the answer to that question might make no sense
on a high level.

On the other hand, we could compare the models by their scores
on a "Scholastic Aptitude Test" or in how well they do in a
Parliamentary debate situation.  

I don't believe any of this, anyway.  If a brain were indeed
significantly chaotic, it probably wouldn'y work.

  
